The Runtime Theory
mediumLeetCode#fast-slow#floyd-cycle

Find the Duplicate Number

Find the repeated value in n+1 integers ranging from 1 through n without modifying the array or using extra space.

The Runtime Theory Team25 min read
Solve it

Solving happens on the judge — come back and mark it done

Sample cases

innums=[1,3,4,2,2]

out2

innums=[3,1,3,4,2]

out3

innums=[1,1]

out1

Find the repeated value in n+1 integers ranging from 1 through n without modifying the array or using extra space.

A good solution should

  • State the invariant or decision rule that makes the approach correct.
  • Explain the time and space complexity in terms of the input sizes and required output.
  • Handle empty, minimal, duplicate, and boundary-shaped inputs covered by the contract.

Reasoning prompt

Treat each value as the next index to visit. Prove that the induced sequence contains a cycle and locate its entry.

Use the linked judge for the canonical problem. The examples above are compact TRT checks; write additional cases before submitting, especially for the boundary that tends to break your chosen invariant.

More practice in this topic

medium · linked listsAdd Two Numbersmedium · linked listsCopy List with Random Pointereasy · linked listsLinked List Cycle

One dispatch a week

The trace behind each problem, the tradeoff that explains it, and one technical dispatch per week — no noise.

One technical dispatch per week. No noise.

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